Characterizations and Infinite Divisibility of Certain Recently Introduced Distributions IV

Certain characterizations of recently proposed univariate continuous distributions are presented in different directions. This work contains a good number of reintroduced distributions and may serve as a source of preventing the reinvention and/or duplication of the existing distributions in the future

A New Weibull–Pareto Distribution: Properties and Applications

Many distributions have been used as lifetime models. In this article, we propose a new three-parameter Weibull–Pareto distribution, which can produce the most important hazard rate shapes, namely, constant, increasing, decreasing, bathtub, and upsidedown bathtub. Various structural properties of the new distribution are derived including explicit expressions for the moments and incomplete moments, Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, and generating and quantile functions. The Rényi and q entropies are also derived. We obtain the density function of the order statistics and their moments. The model parameters are estimated by maximum likelihood and the observed information matrix is determined. The usefulness of the new model is illustrated by means of two real datasets on Wheaton river flood and bladder cancer. In the two applications, the new model provides better fits than the Kumaraswamy–Pareto, beta-exponentiated Pareto, beta-Pareto, exponentiated Pareto, and Pareto models

The Transmuted Weibull-Pareto Distribution

A new generalization of the Weibull-Pareto distribution called the transmuted Weibull-Pareto distribution is proposed and studied. Various mathematical properties of this distribution including ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves and order statistics are derived. The method of maximum likelihood is used for estimating the model parameters. The flexibility of the new lifetime model is illustrated by means of an application to a real data set

Some Extended Classes of Distributions: Characterizations and Properties

Based on a simple relationship between two truncated moments and certain functions of the th order statistic, we characterize some extended classes of distributions recently proposed in the statistical literature, videlicet Beta-G, Gamma-G, Kumaraswamy-G and McDonald-G. Several properties of these extended classes and some special cases are discussed. We compare these classes in terms of goodness-of-fit criteria using some baseline distributions by means of two real data sets

Equilibrium, Adverse Selection, and Statistical Distributions

This paper addresses the problem of multiple equilibria in markets with adverse selection. Akerlof (1970) identified an unique equilibrium of the total market failure under adverse selection. Posterioly, Wilson (1979, 1980) argued that the presence of adverse selection may lead to multiple equilibria. In particular, this paper extends the work of Rose (1993), who stated that the existence of multiple equilibria depends on the distribution of quality. Rose found that multiple equilibria are highly unlikely for most standard probability distributions. This work considers additional statistical distributions for quality. The simulation results suggest the existence of multiple equilibria when the quality follows a beta normal distribution.Adverse Selection; Multiple Equilibria; Statistical Distributions; Akerlof-Wilson Model.